Coefficient of 'Kinetic' Rolling Friction(?)

When looking at rolling objects, the force of rolling resistance is determined by a coefficient of rolling friction. Is this coefficient constant for an object when both stationary and moving? Or is there a separate static and kinetic coefficient as there is with sliding friction?

I am asking this because the research I have done into this so far, I have only found talk of just the one coefficient. However an object on wheels much surely require a larger force for initial acceleration from stationary than to maintain velocity once in motion? If you could recommend any literature on this subject that would be very kind, I have searched through a number of books on Statics but can't seem to find much information.

It should be called rolling resistance, not rolling friction, since that can cause it to be confused with actual friction (static or dynamic).

You could consider "static" rolling resistance to be related to the amount of torque or force it takes to overcome a "flat' spot at the bottom of the wheel if it's been at rest for some time. For example a cold tire on a car that's been at rest overnight. Normally rolling resistance is considered a constant fraction of the weight on the wheel (or the force between tire and pavement). It may vary a bit with speed, but I don't know the formula.